Third normal formWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesC, D, F -> GG -> DA -> GA, D -> BA, D -> CE -> C, DA, E -> C, GE -> GThe first step in computing the normal form, is to derive a canonical (minimal) set of functional dependencies. We have already done this first step for you. The following is a set of canonical functional dependencies (for the dependencies shown above):G -> DC, D, F -> GA -> BA -> GE -> CE -> GA -> CWe have also computed the minimal keys for you:{A, E, F}Apply the synthesis algorithm to derive a third normal form for the relation R(A, B, C, D, E, F, G).Write your answer as followsWrite one relation/table per line, for example, like:Relation1(A,B)Relation2(B,C,D)
Question
Third normal formWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesC, D, F -> GG -> DA -> GA, D -> BA, D -> CE -> C, DA, E -> C, GE -> GThe first step in computing the normal form, is to derive a canonical (minimal) set of functional dependencies. We have already done this first step for you. The following is a set of canonical functional dependencies (for the dependencies shown above):G -> DC, D, F -> GA -> BA -> GE -> CE -> GA -> CWe have also computed the minimal keys for you:{A, E, F}Apply the synthesis algorithm to derive a third normal form for the relation R(A, B, C, D, E, F, G).Write your answer as followsWrite one relation/table per line, for example, like:Relation1(A,B)Relation2(B,C,D)
Solution
To derive a third normal form (3NF) for the relation R(A, B, C, D, E, F, G) using the synthesis algorithm, we first need to identify the candidate keys. From the given information, we know that the candidate keys are {A, E, F}.
Next, we create a relation for each functional dependency:
Relation1(G, D) Relation2(C, D, F, G) Relation3(A, B) Relation4(A, G) Relation5(E, C) Relation6(E, G) Relation7(A, C)
Now, we need to ensure that each relation satisfies the 3NF conditions.
3NF conditions are:
- All the attributes in a relation must have their values determined by the key, the whole key, and nothing but the key.
- There should be no transitive dependency for non-prime attributes.
Checking each relation:
Relation1(G, D): G is the key and determines D. So, it is in 3NF.
Relation2(C, D, F, G): Here, {C, D, F} is the key and determines G. So, it is in 3NF.
Relation3(A, B): A is the key and determines B. So, it is in 3NF.
Relation4(A, G): A is the key and determines G. So, it is in 3NF.
Relation5(E, C): E is the key and determines C. So, it is in 3NF.
Relation6(E, G): E is the key and determines G. So, it is in 3NF.
Relation7(A, C): A is the key and determines C. So, it is in 3NF.
Therefore, all the relations are in 3NF.
Similar Questions
Boyce-Codd normal formWe have the attributes: {A, B, C, D, E}.Consider the following functional dependenciesC -> A, ED -> AA, B -> C, EE -> AC -> BThe first step in computing the normal form, is to derive a canonical (minimal) set of functional dependencies. We have already done this first step for you. The following is a set of canonical functional dependencies (for the dependencies shown above):C -> BE -> AD -> AA, B -> EC -> AA, B -> CWe have also computed the minimal keys for you:{C, D}{B, D}Apply the synthesis algorithm to derive a Boyce-Codd normal form for the relation R(A, B, C, D, E).Write your answer as followsWrite one relation/table per line, for example, like:Relation1(A,B)Relation2(B,C,D)
We have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesB, E -> C, D, FA, G -> B, CA, F -> B, DF, G -> ED, E -> A, B, GD, E -> A, BThe first step in computing the normal form, is to derive a canonical (minimal) set of functional dependencies. We have already done this first step for you. The following is a set of canonical functional dependencies (for the dependencies shown above):B, E -> DD, E -> AA, F -> DA, F -> BA, G -> BB, E -> FF, G -> EA, G -> CD, E -> GApply the synthesis algorithm to derive a Boyce-Codd normal form for the relation R(A, B, C, D, E, F, G).Write your answer as followsFunctional dependencies: write one dependency per line, for exampleA,B -> CB,C,D -> A,FSplitting steps: write one split per line, for examplespliting R(A,B,C,D) into S(A,B,C) and T(A,D) -- the relation names are not importantspliting (A,B,C) into (A,B) and (A,C) -- and can even be omitted...
1. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesA, C, F -> D, EA -> CA, C, F -> B, EF -> A, BA, C -> E, F, GA, F, G -> C, DB, C -> DB -> AThe minimal keys are:{B}{F}{A}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form2. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesF -> E, GA, G -> C, D, EA, B -> FD -> F, GB, E, F -> D, GA, D, E -> B, FB, D, F -> A, EF, G -> B, D, EThe minimal keys are:{D}{F}{A, B}{A, G}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form3. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesB, C, D -> E, GB -> A, ED, E -> CA, C -> B, D, EB -> C, DD, F, G -> AG -> BB, C -> FThe minimal keys are:{B}{G}{A, C}{A, D, E}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form4. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesA, F, G -> CC, F -> GB -> C, FA, D, E -> CE, F, G -> B, CA, B, F -> D, E, GB, C -> A, DA, C, F -> GThe minimal keys are:{B}{C, E, F}{E, F, G}{A, D, E, F}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form5. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesD -> BF -> AB, C, D -> E, FA -> GE, F -> CA, D -> E, FE, F -> GC, F -> A, EThe minimal keys are:{D, F}{C, D}{A, D}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form6. Normal formsWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesC -> EE -> D, GD -> FF -> B, GF -> C, D, EG -> FC -> FC, G -> EThe minimal keys are:{A, E}{A, C}{A, F}{A, G}{A, D}Determine whether these functional dependencies are in the following normal form(s):Boyce Codd normal form
Which normal form deals with the elimination of transitive dependencies?Question 10Answera.Boyce-Codd Normal Form (BCNF)b.Third Normal Form (3NF)c.First Normal Form (1NF)d.Second Normal Form (2NF)
Which of the following normal forms is achieved when all non-key attributes are fully functionally dependent on the primary key?Question 11Answera.Second Normal Form (2NF)b.Boyce-Codd Normal Form (BCNF)c.First Normal Form (1NF)d.Third Normal Form (3NF)
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